I learnt on a BMX but I can bunny hop on 24/26 inch wheels to, the skill is transferable one you get the feel for the lean back.

A bunny hop is not a bouncing action... although you CAN get the bike off the floor in this method - I call that method hoppity hops, it's incorrect and will hurt your wrists. You can hop with suspension if your bike has it, not the same thing.

The bunny hop is serveral movement that blend into one.

 1. Throw your weight backwards (do not pull up on bars)
 2a. Push UP and FORWARD on the bars.
 2b. Jump hard, focusing on tucking your legs as close to your body as you can.

Now to explain why this works...

Throwing your weight backwards is more effective than using your muscles to lift the bike, you also have to have your weight behind the back wheel to pop up the front. So stick your bum out.

Pushing up gives you more height and pushing forward brings the back wheel up.

Tucking your legs brings the back wheel up even further, this is an explosive movement, you should bring them up as hard and fast as you can. You need peddles which actually have pins that aren't worn out or you can slip a foot.
I find that you don't need to focus on pushing back with you feet to keep grip, you naturally wind up doing it when you push forward on the bars and crunch legs.

It took me a while to get the technique correct, I started jumping over a single flat 2x4. Then after I got comfortable doing that I put the 2x4 on it's side, to double height... then just progressed like that.

Practise required! It's not very fun at first but once you get down the technique and start making some progress it's very satisfying!